I can access the BCL from the OpenStudio Application but it does not have the same options as the online BCL. How do I get components from the online BCL into my Application?

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Select "Find Components" under the Components and Measures menu item. A BCL dialog will pop up, and you'll find construction assemblies as one of the categories you can select from. You'll have to skim through several to find one that meets your needs, but once you pick and download it, it will be available in your library under the constructions tab to drag and drop into your model.

This video may help explain things.

One thing to keep in mind; if you are on the BCL website and for example under Construction Assemblies, is that when you search, the items returned are no longer limited to "Construction Assemblies". In fact when I search for "Steel R-19" the top item is a Material for framing cavity. If you want to get that in the GUI you need to get it as a material, not a construction, but it just represents the cavity later, it needs sheathing. This happens with either the main search dialog in the blue bar or the "Enter Terms" search dialog.

Here is a screenshot prior to search (the seach dialog is populated but has not be run yet)

And this is post search. Notice the top item isn't a selection. That may be what you are seeing?